One question of great experimental and theoretical interest is whether quantum gravity can produce inflationary models with relatively large values of \(r\) , the tensor to scalar ratio. Future experiments promise to greatly tighten the upper bound on \(r\)  down to around \(r \le 10^{-3}\)  [1]}, [2]}. So the question is whether quantum gravity, or string theory, allow models with \(r> 10^{-3}\) , which are values potentially measurable in the near future.
The value of \(r\)  is related to the total amount of displacement experienced by the inflaton field as it slowly rolls down the potential [3]}.
At the level of effective field theories we can have relatively large values of \(r\) , and the simple power law potentials have already been excluded by the present constraints.
In string theory, the first models suggested a very small value for \(r\) , but subsequently other proposals suggested larger values, see [4]}, [5]}. However, it is possible that there is a theoretical upper bound for \(r\)  and it would be very interesting to understand where it is.
